Consider the autonomous differential equationy'(t)=f(y(t)), wherefis a differentiable function. Lety*be such thatf(y*)=0.

Why is it that iff'(y*)<0theny*is a (asymptotically) stable equilibrium?

Thanks in advance.

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- Jun 29th 2010, 06:33 PMJoachimAgrellStability criterion for autonomous ODE equilibria
Consider the autonomous differential equation

*y'(t)=f(y(t))*, where*f*is a differentiable function. Let*y**be such that*f(y*)*=0.

Why is it that if*f'(y*)<0*then*y**is a (asymptotically) stable equilibrium?

Thanks in advance.